11 comments:

Giotis
said...

I watched recently on TV Clifford and Kaku in a documentary about the origin and structure of the Universe. In a particular scene he was near a street band; the band was playing and Clifford (elaborating on the musical metaphor of string theory) was explaining that with branes the string theory "band" has expanded and containes not only stringed instruments but also drums (meaning the branes).

I thought, yes ok, but it seems to me that the band is out of rhythm and is lacking a maestro.

In the same documentary Kaku was making bubbles in a NYC street; people around him seemed puzzled. I think he was explainaning something about the bubble universe.

Here’s an analogy to understand this: imagine that our universe is a two-dimensional pool table, which you look down on from the third spatial dimension. When the billiard balls collide on the table, they scatter into new trajectories across the surface. But we also hear the click of sound as they impact: that’s collision energy being radiated into a third dimension above and beyond the surface. In this picture, the billiard balls are like protons and neutrons, and the sound wave behaves like the graviton.

.....maybe Clifford was elaborating more on "the sound of the billiard balls" as an extension of, or maybe, even in context of a metal sheet? Of course, I can't speak for him.

Intuition and Logic in Mathematics by Henri Poincaré

On the other hand, look at Professor Klein: he is studying one of the most abstract questions of the theory of functions to determine whether on a given Riemann surface there always exists a function admitting of given singularities. What does the celebrated German geometer do? He replaces his Riemann surface by a metallic surface whose electric conductivity varies according to certain laws. He connects two of its points with the two poles of a battery. The current, says he, must pass, and the distribution of this current on the surface will define a function whose singularities will be precisely those called for by the enunciation.

Historically again, one had to know where this pursuance of the geometers arose from, to want to unite natural things with such abstract thinking?:)

If you cannot grasp this tendency in expression "such relations" will remain purely abstract for you. Not real.

I think such tendencies were part of the quest to see in relationship too, as extensions of Poincaré's travels? I'm wondering here?

"The gravitons behave like sound in a metal sheet," says Dvali. "Hitting the sheet with a hammer creates a sound wave that travels along its surface. But the sound propagation is not exactly two-dimensional as part of the energy is lost into the surrounding air. Near the hammer, the loss of energy is small, but further away, it's more significant."

So one assumes then that such graduations have indeed taken place to the non-euclidean realms, to see dynamical processes in close association with nature, in expression.

Oh one more thing here for consideration. It requires mental movement in abstract ways for such things to make sense while correlating with nature?:)

We are told that "mathematics is that study which knows nothing of observation..." I think no statement could have been more opposite to the undoubted facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activity of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world, ...that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of imagination and invention. ...Were it not unbecoming to dilate on one's personal experience, I could tell a story of almost romantic interest about my own latest researches in a field where Geometry, Algebra, and the Theory of Numbers melt in a surprising manner into one another.James Joseph Sylvester

Historically this is the advance of Poincaré and those geometers who saw further mathematically modelling in the extreme, yet, necessary?

I have found the most interesting of your this and thats of late to be found in the side bar, rather than here in the post, with tweets of the book case and the CD rack being sold. Most interesting of all is your lorem ipsum, for it appears so paradoxical. That being since Cicero maintained pleasure as being something found only in a stolen moment, with you reminding that life with only reason is hollow, why then would anyone choose theoretical physics as a vocation; for it would appear to only further restrict such moments? Perhaps this suggests we should extend our definition of what’s required to be a good theorist, from one that is able to endure pain, to one that actually enjoys it :-)

Remembering the lesson solidifies opinion of what is presented for examination?

Even Albert Einstein needed help occasionally. In 1912, when Einstein first realized that a new kind of geometry was needed to describe space and time, he had little idea of how to proceed. Fortunately, he shared his difficulties with a mathematician friend, Marcel Grossman, who knew just what Einstein needed and introduced him to the work of the mathematician Bernhard Riemann. It took Einstein three more years to work out the full theory, but Grossman was right, and this was a critical point in the development of general relativity. Doing Science in the Open

A comment from NYT on Paul Krugman's latest column (Aug 28) goes like this: (I wonder if the numbers are right)

Dr. Krugman's nuanced assessment is correct, but regardless of the details, the US economy faces serious danger that will not easily be overcome. That's because the true basis of the economic catastrophe here is cultural— the undermining of compassion, fair play, and the most basic sense of proportion in favor of outrageous greed, viciousness, and corruption in high places. Our economy is now a cruel, exploitative, predatory system of excessive crony capitalism.

As an old engineering professor, I'm on the front lines of this horrific debacle— my field has been eviscerated with particular ferocity. I teach a young American generation condemned to dismal indentured servitude- outsourcing and the H1B have decimated engineering in North America, since foreign grads, as in India, finish schooling with little debt and much lower cost-of-living.

My students by contrast, are inevitably saddled with staggering debt in their grueling years of training. Those drowning in student loans are “lucky”— if they also suffer injury, auto accident or crime (as victims, not perpetrators), then the vultures in our corrupt financial, health care and legal systems prey upon them relentlessly, reducing them to virtual serfdom (aggravating our recession by draining capital away from consumers and true producers). The brightest graduates suffer the most, and if they slip at any point, rather than being helped, they’re kicked harder and harder while down— apparently the highest “virtue” in our plutocratic Potemkin economy. As a further insult, they are confronted with usurious interest rates and then denied employment due to their credit ratings and unavoidable debt just to be trained— practices so outrageous, they are harshly punished as felonies elsewhere in the world.

Unsurprisingly, my students vote with their feet— by the spring of 2009, 40% were inclined to emigrate from the USA. They leave for engineering hubs like Korea, Japan, China, Belgium, Holland, Germany, France or Sweden, but also places like South America. Why? These are far better places to raise kids, and they cherish talent and creativity rather than squandering human capital in the neo-feudalism that now rules the USA. Only Britain and Australia suffer similar brain drains, mainly since they have adopted much of our own brand of neoliberalism and predatory capitalism.

My parents, immigrants to the USA decades ago, would weep if they saw what we have become. For young engineers, the future global languages of our field (and the sciences in general) will be Chinese and German, and anyone in the field would be well-advised to learn one (or both) of them to technical standard, write your papers and even found journals in them, whether or not you emigrate.

Commonsense and maddeningly obvious reforms, thus far stifled, are needed at once for these outrages and excesses that have stolen so much from the American populace. Our moneyed elites fail to realize that revolutions have started over far less.

You know what is really sad about that: that that's hardly news. To look at it from the bright side though, during the last decade, Americans by and large have become noticeably less arrogant and ignorant. They know their health care sucks. They know their school education doesn't score well in international comparisons. They know their poverty rate, esp among children, is higher than in most modern civilizations. They have relearned their economy isn't immune to slumps, and that their standard and quality of living is by no means exceptional. In short, they have learned some modesty. Now they have to draw the conclusions from it.

Well said Bee. Fortunately Europe overall resist to the American economical model and did not adopt brutal capitalism. The rise of right wing parties in Europe could be attributed not to the fact that people approve extreme economical liberalism but to the general feeling that these parties are guardians of the national identity. In contrast the socialist parties in Europe are related in people's mind to a stronger and more unified Europe. Europeans are afraid that they'll lose their national identity; that's all. It is natural and understandable. The immigration issue played also an important role.